Questions: Which of the following values cannot be probabilities? 0, 5 / 3, 1.29, 3 / 5, 0.02, sqrt(2), -0.47, 1 Select all the values that cannot be probabilities. A. 1 B. 0.02 C. -0.47 D. 1.29 E. 0 F. 3/5 G. 5/3 H. sqrt(2)

Solution Steps

To determine which values cannot be probabilities, we need to remember that probabilities must be between 0 and 1, inclusive. Any value outside this range cannot be a probability.

We are given the following values to evaluate as potential probabilities: \[ 0, \frac{5}{3}, 1.29, \frac{3}{5}, 0.02, \sqrt{2}, -0.47, 1 \]

A valid probability must satisfy the condition: \[ 0 \leq P \leq 1 \] Thus, any value less than 0 or greater than 1 cannot be a probability.

• \(0\) is valid.
• \(\frac{5}{3} \approx 1.6667\) is invalid.
• \(1.29\) is invalid.
• \(\frac{3}{5} = 0.6\) is valid.
• \(0.02\) is valid.
• \(\sqrt{2} \approx 1.4142\) is invalid.
• \(-0.47\) is invalid.
• \(1\) is valid.

The values that cannot be probabilities are: \[ \frac{5}{3}, 1.29, \sqrt{2}, -0.47 \]

Final Answer